Clustering of charged colloidal particles in the microgravity environment of space

We conducted a charge–charge clustering experiment of positively and negatively charged colloidal particles in aqueous media under a microgravity environment at the International Space Station. A special setup was used to mix the colloid particles in microgravity and then these structures were immobilized in gel cured using ultraviolet (UV) light. The samples returned to the ground were observed by optical microscopy. The space sample of polystyrene particles with a specific gravity ρ (=1.05) close to the medium had an average association number of ~50% larger than the ground control and better structural symmetry. The effect of electrostatic interactions on the clustering was also confirmed for titania particles (ρ ~ 3), whose association structures were only possible in the microgravity environment without any sedimentation they generally suffer on the ground. This study suggests that even slight sedimentation and convection on the ground significantly affect the structure formation of colloids. Knowledge from this study will help us to develop a model which will be used to design photonic materials and better drugs.

experiment for the following reasons.
The sample container is made of the plastic film bag shown in Figure 2 of the main text. Under microgravity, the container bag is considered to have a shape that balances the internal pressure of the sample liquid and the force due to the elasticity of the plastic film of the sample bag. Since the effective G at the re-boost was sufficiently small compared to the internal pressure of the liquid, the deformation of the container is considered negligible. Also, the sample is sealed in a bag and has no free surface. For these reasons, we assume that the flow due to G is negligible.
Without flow inside the sample, all particles are subjected to a force in the direction of G and should move accordingly. Supplementary Figure 3 illustrates the effect of sedimentation. Although the travel distance ~3 microns is indeed larger than the particle diameter (1 micron), we believe that the re-boosting effect is negligible except near the sample bag walls if all the particles in the sample move in the same direction.
The portion of the space sample near the sample bag wall remained liquid in many cases, due to insufficient gelation. In addition, microscopic observations were made by cutting the sample with a scalpel and observing the cross section. Thus, since the portion of three microns from the sample bag surface was excluded from the evaluation, we assume that the effect of sedimentation by the reboost was considered negligible in practice.

Synthesis of positively charged polystyrene particles
Positively charged PS particles were synthesized by dispersion polymerization 2,3 as follows: 10.0 g of polyvinylpyrrolidone (PVP K30, Wako Pure Chemicals, Tokyo, Japan) was dissolved in 126 mL of ethanol and 14 mL of Milli-Q water with stirring and bubbled with N2 gas. To this reaction solution, the solution was added 0.136 g of 2,2'-azobis(isobutyronitrile) (AIBN, Wako), 0.2 g of the cationic monomer 4-vinyl benzyl trimethylammonium chloride, 0.2 g of the red fluorescent dye Nile Red (Wako), 10 mL of the monomer styrene, and 0.5 mL of the divinylbenzene (Wako) were added in this order. The mixture was stirred in an oil bath at 70 °C for 24 hours. We determined the particle diameter by using a scanning electron microscopy.

Synthesis of titania particles
A partially modified sol-gel method for synthesizing titania particles using titanium tetraisopropoxide as starting material by Tanaka et al. 4 . A mixture of 2100 mL of methanol and 900 mL of acetonitrile was used as the solvent. To this solution were added 4 mL of Milli-Q water, 22.4 g

Introduction of fluorescent dyes
Fluorescent dyes were introduced to the particles using the method of Van Blaaderen and Vrij 5 .
For the positively charged particles, 2.5 mg of Rhodamine B-isothiocyanate (RITC, Sigma Aldrich, Missouri, U.S.A.) was dissolved in 2 mL of ethanol, to which 10 µL of 3-aminopropyltriethoxysilane (APTES, Shin-Etsu Chemical, Tokyo, Japan) was added in tiny drops. The mixture was then stirred for 24 hours. in a light-shielded condition. The compound (RITC-APTES) was obtained by adding RITC to the amino group APTES. Next, 13 mL of ethanol, 4.3 mL of Milli-Q water, 430 µL of tetraethoxysilane (Shin-Etsu Chemical), and 100 µL of RITC-APTES solution were added to a Teflon vessel and stirred. To this was added 620 µL of 28% ammonia water and 10 mL of titania particle dispersion (5 vol%, ethanol dispersion) and went for 24 hours. After the removal of unreacted material by centrifugation, the particles were dispersed in 30 mL of ethanol. Fluorescein-4-isothiocyanate (FITC, Wako) was introduced.

Modification by polyelectrolytes
To synthesize titania p-particles, we modified the particle surfaces with polyethyleneimine. 13 mL of ethanol and 4.3 mL of Milli-Q water were mixed as a solvent. 1.5 mL of a 50% solution of trimethoxysilylpropyl modified polyethyleneimine (solvent isopropanol, Gelest, Pennsylvania, U.S.A.) and 28% 620 µL of ammonia water were added and stirred, followed by the addition of 10 mL of titania particle dispersion with RITC and stirred at room temperature for 24 hours. The reaction solution was centrifuged to remove impurities, and the particles were dispersed in Milli-Q water.
Titania n-particles were prepared by modifying the particle surfaces with sodium poly (styrene sulfonate). First, vinyl groups were introduced onto the particle surfaces as follows. 30 mL of Fluorescein-loaded titania particle dispersion, 350 µL of γ-methacryloxypropyltrimethoxysilane (TPM, Shin-Etsu Chemical), and 850 µL of 28% ammonia water were added to a 200-mL flask and stirred for three hours. Then 20 mL of ethanol was added, and the ammonia was removed using an evaporator at 55~60 ºC. The sample was redispersed in 30 mL of 70% EG after removing unreacted material by centrifugation. Poly(styrene sulfonate) sodium salt was then introduced by the following method: 1.0 g of styrenesulfonate sodium salt (NaSS) was dissolved in 60 mL of 70% EG, 30 mL of the above vinyl group introduced silica particle dispersion was added and bubbled with N2 gas for 15 minutes. Next, 35 mg of 2,2'-Azobis[2-methyl-N-(2-hydroxyethyl)propionamide], a radical polymerization initiator, was dissolved in 10 mL of 70% EG, bubbled with N2 gas for 10 min, and the entire amount was dropped into the reaction solution and stirred overnight. The product was purified by centrifugation and dispersed in Milli-Q water.

Gelation reagents
We have previously the immobilization of charged colloidal crystals using acrylamide and Nmethylolacrylamide gel (NMAM) polymer gels 6 . However, the clustering of positive and negative particles was inhibited by the presence of NMAM, presumably due to slight hydrolysis of the NMAM molecules in the gelator solution, resulting in ionic impurities, so we choose to use dimethyl acrylamide (DMA) as a gel monomer that is less susceptible to hydrolysis.

Numerical simulation by Monte Carlo method
Monte Carlo simulations of the clustering were carried out to calculate the distribution of the number of associations. The calculated results agree with the results of Brownian dynamics simulations (see reference 7 for more details).

Simulation method
Numerical simulations have been carried out for a system of charged colloidal particles interacting with the Yukawa-type potential by applying the Monte Carlo method for canonical ensemble and using the Metropolis algorithm. Assuming the ergodic nature of the system, the steady-state distribution of particle configurations ωs as, and the Yukawa-type potential uij acting between particle i and particle j, using the thermal energy kBT, the Bjerrum length lB, and the Debye shielding length !" , is as follows where # is the Boltzmann constant, Bjerrum length # = (e is the elementary charge), and e is the dielectric constant of the solvent. The Debye length !" is defined by ) = 4 # using the total ionic concentration C in solution. The total potential energy * at state s is * = ∑ if it is approximated as the sum of pair potentials. In equation (1), . is the coordination integral, which under constant volume and temperature is given as where * . = " ) ⋯ . is the volume element concerning the position { " , ) , … , . } * in state s of N particles in the system. Also, if we define the transition probability from state t to state s as /* , the steady-state distribution of particle configurations from Eq.(1) as In equilibrium, the transition probability is expressed by the following detailed balance, as is satisfied. The Metropolis algorithm below achieves thermal equilibrium conditions in the system by sampling particle configurations to satisfy this detail balance.

Metropolis algorithm
In a Monte Carlo simulation using the Metropolis method, the transition probability is determined by the energy difference between state t and state s. If * < / , the system transitions from state t to state s with probability 1; if * > / , the system transitions from state t to state s with probability exp(− [ * − / ]) (< 1). The specific method is as follows: for the nth time, let the system be in state t. Select one particle of the system at random, and let its particle number be α and its position vector is 0 = ( 0 , 0 , 0 ).
(a) The displacement vector Δ 0 = (Δ 0 , Δ 0 , Δ 0 ) is prepared and the particle α is moved from In this study, we use uniform random numbers 1 , 2 , and 3 in the interval (0,1], In this study, d = 1 (i.e., δ is equal to the particle radius). (e) The state t determined in this way is the n+1st time, and the process starts again from (a). These operations are repeated until the system converges to an equilibrium state.

Numerical simulation conditions
We mainly used the conditions listed in Supplementary The equilibrium state was determined to have been reached when the total potential energy became constant. In this study, the distribution of the number of associations was obtained from the system judged to have reached equilibrium. Simulations were performed for a system with NA=20 positively charged particles and NB=500 positively charged particles. We used periodic boundaries as the boundary conditions of the system.

Structural Symmetry for Clusters of m = 2 and m = 3
The structural symmetry of tetrahedral clusters (m=4) of polystyrene particles is discussed in the main text(p.10)The bond orientation order parameter qtetra, and we observed that the space sample has better symmetry. For clusters of m=3 and m=2, we defined q3 and q2, as in the case of tetrahedral clusters. On the other hand, q2 showed no clear dependence on [NaCl] for both space and ground samples, ranging from 0.6 to 0.8. This suggests that the contribution of electrostatic repulsive force to the aggregate formation is not significant due to the long distance between adhering particles. In such cases, the effect of microgravity is considered to be small.
The measure of symmetry, other than q3 and q2, is the sum of the bond vectors, |r3|and |r2|; regardless of m, if the generated cluster is perfectly symmetric, the sum of the bond vectors takes the minimum value of zero, and the better the symmetry, the smaller its value. Figure 7 shows the |r3|and |r2| for space and ground samples, respectively. The same conclusions regarding the effects of [NaCl] and microgravity on the structural symmetry of the clusters were obtained using as when using q3 and q2. particles. Supplementary Figure 9 shows the distribution of z potentials. It is assumed that the positively charged polyelectrolyte modifies the titania particle surface decreases as the silica leaches out, decreasing the number of charges. Because the surface of pure silica is slightly negatively charged in water, the particles become negatively charged when the polyelectrolyte is significantly removed.

Degradation of titania particles
However, as shown in Supplementary Figure 9, no charge reversal of the particles was observed.
Note that titania particles act as photocatalysts. Therefore, if the surface silica layer was partly lost and the titania core surface appeared, the UV irradiation during gel fixation may have decomposed the rhodamine and faded the color. The change in fluorescence color observed in the space experiment may also be explained by the desorption of the silica layer.
The leaching and desorption of the silica layer are expected to change the interactions between particles as follows. (1) The electrostatic repulsive force between p-p and n-n particles and the attractive electrostatic force between p-n particles decrease due to the reduced number of charges.
Also, (2) since the magnitude of the vdW interaction between particles is approximately proportional to the refractive index difference between the material and the medium, the vdW force between particles increases as the silica layer, which has a lower refractive index than titania, becomes thinner.
Potential calculations considering (1) and (2) suggest that the contribution of the vdW attraction force exceeds the electrostatic repulsion force and that the vdW force may cause aggregation between n-n particles and between p-p particles. The ground control sample also observed that particles with the same sign charge formed macroscopic aggregates.
However, from the potential calculations, it is concluded that for the vdW force to exceed the electrostatic repulsive force between the particles, a large portion of the silica coat layer of the particles must be desorbed and dissolved, which is not consistent with the amount of silica dissolved (about 25% of the total amount). The partial desorption and dissolution of the silica coat layer may have created patchy, negatively charged silica regions on the surface of the positively charged particles. In this case, even though the total charge of the particles is positive, the particles may attract each other because of attraction between local positive and negative charged regions.

Determination of the dissolved silica concentration
Cut gel pieces of the space experimental samples were immersed in Milli-Q water and shaken for two days to extract the silicate dissolved in the liquid inside the sample gels. The amount of silica concentration in the extract was determined using the molybdenum blue method 8 . In an acidic sulfuric acid solution, the silicate reacts with ammonium molybdate(VI) tetrahydrate ((NH4)6Mo7O24) to form a yellow heteropoly acid. This was reduced to form molybdenum blue, and the absorbance was measured at 810 nm in a spectrophotometer. The silicate concentration of the sample was determined after heating at 80°C for 1 hour in 1M NaOH to hydrolyze the polysilicon acid.

Supplementary Figures
Supplementary Figure 1

Si Kα1
Ti Kα1 Supplementary Figure 9 An example of the distribution of ζ potential of ground-controlled TiO2(+) (TiO2#23) particles. The distribution of ζ potentials was examined by electrophoresis experiments on ground control samples of TiO2 (+) particles that were not fixed in a gel. The average value of the potential of the space sample was lower than that of the ground control sample, but the charge did not invert to become negative.

Supplementary Figure 10
The MC simulation on the effect of particle size distribution on the distribution of m. The distribution of m at various values of Cs for (a)monodisperse and (b) polydisperse (particle size distribution = 4% in standard deviation) polystyrene clusters. The size distribution was assumed to be Gaussian. In the simulations, the surface charge density was assumed as constant. The size polydispersity had a negligible effect on the distribution of m. notisolated notisolated